Analysis and Calculation of Prospective Reserves - Where Payments Depend on the Reserve and a Reserve-Dependent Markov Process

Abstract

Life insurance companies have a great interest in the calculation of prospective reserve since it is an item on the balance sheet of the company. In this thesis, we de ne the prospective reserve such that we can incorporate reserve-dependent payments and such that company made decisions like investment strategies and costs are allowed to depend on the reserve. We study in depth how to calculate the prospective reserve using both analytical and simulation method. We deduce a partial differential equation for the reserve and introduce the two simulation methods: nested simulation and least-squares Monte Carlo simulation, and investigate how to use these methods to calculate the reserve. Furthermore, we calculate the prospective reserve in various examples to illustrate the methods in practice.